Question icon
Grade 12Algebra

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number".

Statement-1 : r is equivalent to either q or p.

Statement-2 : r is equivalent to ~(p ↔ ~q).

Profile image of swati shrivastav
17 Years agoGrade 12
Answers icon

1 Answer

Profile image of ronit bhatiya
17 Years ago

p : x is an irrational number
q : y is a transcendental number
r : x is a rational number iff y is a transcendental number
=> r : ~ p ↔ q
s1 : q or p
s2 : ~ (p↔~q)


p q ~p ~q r:~p↔q s1:q or p p↔~q s2:~(p↔~q)
T T F F F T F T
T F F T T T T F
F T T F T T T F
F F T T F F F T

Based upon above chart
s1 and r are not equivalent
s2 and r are not equivalent